Quantum hydrodynamics in spin chains with phase space methods
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First author draft
Date
2020-05-15
Authors
Polkovnikov, Anatoli
Wurtz, Jonathan
Version
First author draft
OA Version
Citation
Anatoli Polkovnikov, Jonathan Wurtz. "Quantum Hydrodynamics in Spin Chains with Phase Space Methods."
Wurtz J, Polkovnikov A. Quantum diffusion in spin chains with phase space methods. Phys Rev E. 2020;101(5-1):052120. https://doi.org/10.1103/PhysRevE.101.052120.
Wurtz J, Polkovnikov A. Quantum diffusion in spin chains with phase space methods. Phys Rev E. 2020;101(5-1):052120. https://doi.org/10.1103/PhysRevE.101.052120.
Abstract
Connecting short time microscopic dynamics with long time hydrodynamics in strongly correlated
quantum systems is one of the outstanding questions. In particular, it is very difficult to determine
various hydrodynamic coefficients like the diffusion constant or viscosity starting from a microscopic
model: exact quantum simulations are limited to either small system sizes or to short times, which
are insufficient to reach asymptotic behavior. In this Letter, we show that these difficulties, at
least for a particular model, can be circumvented by using the cluster truncated Wigner approximation
(CTWA), which maps quantum Hamiltonian dynamics into classical Hamiltonian dynamics
in auxiliary high-dimensional phase space. We apply CTWA to a XXZ next-nearest-neighbor spin
1/2 chain and find behavior consisting of short time spin relaxation which gradually crosses over to
emergent diffusive behavior at long times. For a random initial state we show that CTWA correctly
reproduces the whole spin spectral function. Necessary in this construction is sampling from properly
fluctuating initial conditions: the Dirac mean-field (variational) ansatz, which neglects such
fluctuations, leads to incorrect predictions.